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A solenoid has a fixed total number of turns N and a fixed cross-sectional area A, but its length L can be changed by adjusting the spacing between windings. How does its self-inductance depend on L?

1. proportional to 1/L²
2. proportional to 1/L
3. proportional to L
4. proportional to L²

Correct answer: proportional to 1/L

Solution

The inductance of a solenoid is L_ind = mu0*N²*A/(length). With N and A held constant, L_ind is inversely proportional to the length. So as length L increases, inductance decreases as 1/L.

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